Digital filters are frequently used for signal processing in systems, such as ultrasound imaging systems, where the set of input data to be processed is limited. In color Doppler imaging, stationary and slowly moving targets produce large, low frequency signals. These unwanted signals need to be removed by a clutter filter in order to detect higher frequency Doppler blood echoes. When a finite impulse response (FIR) digital filter is used, the number of valid output samples is further limited as described below. The limited number of output samples may result in erroneous estimates of signal characteristics. For example, an FIR filter may be used to remove clutter from a Doppler ultrasound signal. The signal characteristic to be estimated is the mean frequency of the Doppler ultrasound signal in the presence of noise. A limited number of output samples can yield a poor estimate of frequency. In an ultrasound imaging system, Doppler measurements are taken at multiple points to produce an ultrasound image. An increase in the number of samples at each point would unacceptably reduce the ultrasound scan rate.
A conventional finite impulse response digital filter receives digital samples of an input signal. The filter includes multiple delay stages. The output of each delay stage is multiplied by a filter coefficient, and the outputs of the multipliers are summed to provide an output sample. When the set of input samples is limited, the number of output samples from the FIR filter depends on both the number of input samples and the number of stages in the filter. For example, when the input data contains sixteen samples and the filter has five stages, or coefficients, the filter provides twelve output samples. An output sample is provided for input samples 1-5, 2-6, . . . 12-16. The number of output samples can be increased by reducing the number of stages, or coefficients, in the FIR filter. However, this "shorter" FIR filter provides less flexibility as to shaping its characteristics and may not remove undesirable components of the input signal.